Tributes continue to be paid at home and abroad to Baroness Thatcher after her death at the age of 87.
David Cameron said she had been a "great Briton" while US President Barack Obama called her a "great champion of freedom and liberty".
The funeral of the former prime minister is expected to be held next week.
The ceremony, with full military honours, will take place at London's St Paul's Cathedral.
Lady Thatcher, Britain's first female premier, was Conservative prime minister from 1979 to 1990 and won three successive general elections.
She died "peacefully" after suffering a stroke while staying at the Ritz hotel in central London.
She will not have a state funeral but will be accorded the same status as Princess Diana and the Queen Mother.
The union jack above Number 10 Downing Street has been lowered to half-mast while Parliament will be recalled from its Easter recess on Wednesday to enable MPs to pay tributes.
After cutting short a trip to Europe to return to London, Mr Cameron described Lady Thatcher as "the patriot prime minister" and the country's "greatest peacetime" leader.
While acknowledging that she had "divided opinion", Mr Cameron said she had "taken a country that was on its knees and made it stand tall again.
"Margaret Thatcher loved this country and served it with all she had," he said. "For that she has her well-earned place in history - and the enduring respect and gratitude of the British people."
Her other successors in No 10 - Sir John Major, Tony Blair and Gordon Brown - paid tribute to her strength of character and political purpose while Labour leader Ed Miliband said Lady Thatcher had been a "unique figure" who "reshaped the politics of a whole generation"
But critics questioned the economic and social impact of her policies, ex-Labour leader Lord Kinnock saying her economic policies had been an "unmitigated disaster for Britain" at the time.
Among international reaction, US President Barack Obama said "America has lost a true friend", while German Chancellor Angela Merkel said she would "never forget her part in surmounting the division of Europe and at the end of the Cold War".
BBC political editor Nick Robinson said Lady Thatcher - who had suffered poor health for several years - would always be a divisive politician but one who inspired "passion" among her critics and supporters.
Her government privatised state-owned industries and was involved in a stand-off with unions during the Miners' Strike of 1984-5.
She was in power when the UK fought a war following Argentina's invasion of the Falkland Islands in 1982 but during her later years in office became associated with Euroscepticism and was increasingly at odds with other senior figures in the Conservative Party.